On the Thermal Energy of Molecular Vortices. 2 1 1 



the quantoid corresponding to A m , then a criticoid is a function 

 wherein the substitution for each coefficient a r of its correspond- 

 ing quantoid A,, causes no change in the function, from which u 

 disappears. Thus defined, critical functions and criticoids are 

 seen to be porismatic in their character. 



" Oakwal " near Brisbane, Queensland, 

 Australia, November 18, 1869. 



XXVII. On the Thermal Energy of Molecular Vortices. By W. 

 J, Macquorn Rankine, C.E., LL.D., F.R.SS.L. $ E., #c* 



§ \.r\BJECT of this Paper.— In a paper "On the Mecha- 

 ^^ nical Action of Heat,'' which I sent to the Royal 

 Society of Edinburgh in December 1849, and which was read 

 in February 1850, it was shown that if sensible or thermometric 

 heat consists in the motion of molecular vortices supposed to be 

 arranged in a particular way, and combined in a particular way 

 with oscillatory movements, the principles of thermodynamics, 

 and various relations between heat and elasticity, are arrived at 

 by applying the laws of dynamics to that hypothesis f. The 

 object of the present paper is to show how the general equation 

 of thermodynamics and other propositions are deduced from the 

 hypothesis of molecular vortices, when freed from all special 

 suppositions as to the figure and arrangement of the vortices 

 and the properties of the matter that moves in them, and reduced 

 to the following form : — That thermometric heat consists in a mo- 

 tion of the particles of bodies in circulating streams with a velocity 

 either constant or fluctuating periodically. This, of course, im- 

 plies that the forces acting amongst those particles are capable 

 of transmitting that motion. 



§ 2. Steady and Periodical Component Motions. — A vortex, in 

 the most general sense of the word, is a stream or current which 

 circulates within a limited space. Conceive a closed vessel of any 

 figure and volume to be filled with vortices or circulating streams, 

 the mean velocity of circulation in each such stream being the 

 same; and let the velocities of the moving particles be either 

 constant or periodic. How complex soever those motions may 

 be, they may be resolved into the following component motions — 

 a motion of steady circulation with the uniform velocity already 

 mentioned as the mean velocity, and a motion consisting in pe- 

 riodical fluctuations of velocity. Those two component motions 

 may be called, respectively the steady circulation and the dis- 

 turbance. 



* From the Transactions of the Royal Society of Edinburgh, vol. xxv. 

 Communicated by the Author. 



f Transactions of the Roval Societv of Edinburgh, 1850, vol. xx. 



P2 



